EtheltheFrog15 In your shoes I would work out what is acceptable, two or three choices, and give your child a limited choice.
But before that I would make sure they don't talk about the party or invite children informally before you are ready to 'do' the invites.
We've had various arguments about my kids saying someone is or is not coming to their party, or someone else saying that they are not coming! It caused one major row and I think all kids do it, but it is best to make the invites official from you so you know what is happening. You can also 'try out' various party guests by having them home for play dates before you send invites to see if your child and this new one do get along.
I have generally let my kids choose who will come to their parties but I have sometimes nudged them towards someone who I know is a good friend but who they have 'forgotten'. Or included someone where they have been invited to someone else's party. I know it sounds sad, tit for tat, but to be fair when they are young friends change and sometimes it is good to just use the party as a way to make new friends! Plus if you are very friendly with a certain mum or dad, and they come to your house a lot, with their kid/s it can sometimes look 'bad' if you don't include their child in the party!
I would avoid parties at home, they are just so much hard work! If you can afford to do a party that includes someone paid to help you, go for it!! My adopted ds and birth dd (who has autistic tendencies) have had...
-Hired bouncy castle in a hired hall (WORST - I worried the whole time someone would get injured on the bouncy castle!)
-Bouncy castle in a leisure centre where the staff supervised it and we did the birthday tea (great)
-Little leisure centre activities in a hired hall, with a party helper, like those little roller carts, things to play on, we did the food (great)
-Supervised go-carts (for 10 year old) where food was provided (Fabulous but very expensive!)
-Farm party where the food was done for us (great)
-Swim party (age 8 and over, fabulous but you really need to know the kids can swim and it is quite hard to organise safely).
We did bowling with my birth child but I agree with sanders re I would avoid football/ gym / ice skating / bowling parties unless you know your DC will cope well with failure / disappointment
Hope it goes well.